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the relation between time t and distance x for a particle moving in a straight line is t=ax 2 + bx where a and b are constants . The retardation is?

the relation between time t and distance x for a particle moving in a straight line is t=ax2+ bx where a and b are constants . The retardation is?

Grade:11

2 Answers

anemous
117 Points
8 years ago
redardation is 2a/(2ax+b)^3
noogler
489 Points
8 years ago
retardation is othing but negative acceleration.
we know that v=dx/dt,al=dv/dt             v=velocity,al=acceleration,x=displacement
first differentiate given eq.w.r.t. t
1=2axdx/dt+dx/dt
1=2axv+bv …..................(1)               v=1/2ax+b
differentiate(1)  w.r.t. t
0=2av2+2axal+bal .....................(2)
substitute v=1/2ax+b in (2)
2a/(2ax+b)2+(2ax+b)al=0
(2ax+b)al= -2a/(2ax+b)2
          al=-2a/(2ax+b)3                                        -ve sign indicates decrease in acceleration
 

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